Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure

Consider a mixed quantum mechanical state, describing a statistical ensemble in terms of an arbitrary density operator $\rho$ of low purity, \tr\rho^2\ll 1, and yielding the ensemble averaged expectation value \tr(\rho A) for any observable $A$. Assuming that the given statistical ensemble $\rho$ is generated by randomly sampling pure states $|\psi>$ according to the corresponding so-called Gaussian adjusted projected measure $[$Goldstein et al., J. Stat. Phys. 125, 1197 (2006)$]$, the expectation value $$ is shown to be extremely close to the ensemble average \tr(\rho A) for the overwhelming majority of pure states $|\psi>$ and any experimentally realistic observable $A$. In particular, such a `typicality' property holds whenever the Hilbert space \hr of the system contains a high dimensional subspace \hr_+\subset\hr with the property that all |\psi>\in\hr_+ are realized with equal probability and all other |\psi> \in\hr are excluded.Comment: accepted for publication in J. Stat. Phy

The Brownian gyrator: a minimal heat engine on the nano-scale

A Brownian particle moving in the vicinity of a generic potential minimum under the influence of dissipation and thermal noise from two different heat baths is shown to act as a minimal heat engine, generating a systematic torque onto the physical object at the origin of the potential and an opposite torque onto the medium generating the dissipation.Comment: Phys. Rev. Lett., in pres

Anisotropic diffusion in square lattice potentials: giant enhancement and control

The unbiased thermal diffusion of an overdamped Brownian particle in a square lattice potential is considered in the presence of an externally applied ac driving. The resulting diffusion matrix exhibits two orthogonal eigenvectors with eigenvalues $D_1>D_2>0$, indicating anisotropic diffusion along a "fast" and a "slow principal axis". For sufficiently small temperatures, $D_1$ may become arbitrarily large and at the same time $D_2$ arbitrarily small. The principal diffusion axis can be made to point into (almost) any direction by varying either the driving amplitude or the coupling of the particle to the potential, without changing any other property of the system or the driving.Comment: 7 pages, 7 figure

Suppression of thermally activated escape by heating

The problem of thermally activated escape over a potential barrier is solved by means of path integrals for one-dimensional reaction dynamics with very general time dependences. For a suitably chosen but still quite simple static potential landscape, the net escape rate may be substantially reduced by temporally increasing the temperature above its unperturbed constant level.Comment: 4 pages, 2 figure

Exploiting lattice potentials for sorting chiral particles

Several ways are demonstrated of how periodic potentials can be exploited for sorting molecules or other small objects which only differ by their chirality. With the help of a static bias force, the two chiral partners can be made to move along orthogonal directions. Time-periodic external forces even lead to motion into exactly opposite directions.Comment: 4 pages, 4 figure

Typical fast thermalization processes in closed many-body systems

Reimann P. Typical fast thermalization processes in closed many-body systems. NATURE COMMUNICATIONS. 2016;7(1): 10821.The lack of knowledge about the detailed many-particle motion on the microscopic scale is a key issue in any theoretical description of a macroscopic experiment. For systems at or close to thermal equilibrium, statistical mechanics provides a very successful general framework to cope with this problem. However, far from equilibrium, only very few quantitative and comparably universal results are known. Here a quantum mechanical prediction of this type is derived and verified against various experimental and numerical data from the literature. It quantitatively describes the entire temporal relaxation towards thermal equilibrium for a large class (in a mathematically precisely defined sense) of closed many-body systems, whose initial state may be arbitrarily far from equilibrium

Optimal evaluation of single-molecule force spectroscopy experiments

The forced rupture of single chemical bonds under external load is addressed. A general framework is put forward to optimally utilize the experimentally observed rupture force data for estimating the parameters of a theoretical model. As an application we explore to what extent a distinction between several recently proposed models is feasible on the basis of realistic experimental data sets.Comment: 4 pages, 3 figures, accepted for publication in Phys. Rev.

Rolling and sliding of a nanorod between two planes: Tribological regimes and control of friction

The motion of a cylindrical crystalline nanoparticle sandwiched between two crystalline planes, one stationary and the other pulled at a constant velocity and pressed down by a normal load, is considered theoretically using a planar model. The results of our model calculations show that, depending on load and velocity, the nanoparticle can be either rolling or sliding. At sufficiently high normal loads, several sliding states characterized by different friction forces can coexist, corresponding to different orientations of the nanoparticle, and allowing one to have low or high friction at the same pulling velocity and normal load.Comment: 5 figure